Theorem 1 ( [1]}) 
A graph \(G(V,E)\)  in the plane is rigid, if and only if there exists a subgraph \(G_1=(V,E_1)\)  where \(E_1\subset E\)  with \(|E_1|=2|V|-3\)  in order that for any \(V_1\subset V\) , the associated induced subgraph \(G_2=(V_1,E_2)\)  of \(G_1\)  with \(E_2\subset E_1\) , satisfies \(|E_2| \le 2|V_1|-3\) .

